unit 2 college physics

magnitude of net force

$$\sqrt{F_x^2 + F_y^2}$$

direction angle

$$\arctan\left(\frac{F_x}{F_y}\right)$$

normal force accelerating upward

m(g+a)

normal force accelerating downward

m(g-a)

acceleration of system $(\text{where }m_1>m_2)$

$$g\left(\frac{m_1 - m_2}{m_1 + m_2}\right)$$

tension

$$m_2(g+a)=m_1(g-a)$$

maximum static friction force

$$\mu_{s}mg$$

maximum deceleration

$$\mu_{s}g$$

braking distance

$$v_0^2+2ad\implies d=\frac{v^2}{2a}$$

reaction distance

$$v\cdot t_{\text{reaction}}$$

parallel to slope (pulling down)

$$mg\sin\theta$$

perpendicular to slope

$$mg\cos\theta$$

maximum angle before sliding

$$\arctan(\mu_{s})$$

normal force on incline

$$mg\cos\theta$$

acceleration down an incline

$$a = g(\sin\theta - \mu_k \cos\theta)$$